The Failure of the ER=EPR Conjecture Under Laboratory Quantum Conditions: A Quantitative Analysis of Null Energy Condition Requirements and Wormhole Non-Traversability

Abstract

The ER=EPR conjecture, proposed by Maldacena and Susskind (2013), posits thatquantum entanglement between two particles is geometrically mediated by a microscopicEinstein–Rosen bridge connecting them. While mathematically elegant within the frame-work of AdS/CFT correspondence and holographic duality, this conjecture faces severe phys-ical contradictions when applied to laboratory-scale quantum systems (electron–positronpairs, photon pairs). This paper provides a quantitative refutation of the ER=EPR hy-pothesis by demonstrating that: (1) maintaining a traversable wormhole throat requiresviolation of the Null Energy Condition (NEC) via exotic matter with negative energy den-sity whose magnitude is ∼ 10116 times greater than any known quantum source of negativeenergy (including the Casimir effect); (2) the Einstein–Rosen bridge metric is dynamicallyunstable and pinches off on a timescale τ ∼ rs/c (∼ 10−43 s for Planck-scale throats), pre-cluding any information transfer; and (3) high-precision quantum measurement experiments(Aspect, Zeilinger, Hensen et al.) have detected no anomalous gravitational signatures, neg-ative energy densities, or spacetime curvature consistent with a wormhole geometry duringwave function collapse. These findings demonstrate that ER=EPR remains a mathemat-ical abstraction applicable only in the semiclassical gravitational regime (large black holeentanglement) and cannot be extrapolated to tabletop quantum mechanics